CS589-04 Digital Image Processing Lecture 5 CS589-04 Digital Image Processing Lecture 5. Morphological Image Processing Spring 2008 New Mexico Tech

Introduction Morphology: a branch of biology that deals with the form and structure of animals and plants Morphological image processing is used to extract image components for representation and description of region shape, such as boundaries, skeletons, and the convex hull 12/3/2018

Preliminaries (1) Reflection Translation 12/3/2018

Example: Reflection and Translation 12/3/2018

Preliminaries (2) Structure elements (SE) Small sets or sub-images used to probe an image under study for properties of interest 12/3/2018

Examples: Structuring Elements (1) origin 12/3/2018

Examples: Structuring Elements (2) Accommodate the entire structuring elements when its origin is on the border of the original set A Origin of B visits every element of A At each location of the origin of B, if B is completely contained in A, then the location is a member of the new set, otherwise it is not a member of the new set. 12/3/2018

Erosion 12/3/2018

Example of Erosion (1) 12/3/2018

Example of Erosion (2) 12/3/2018

Dilation 12/3/2018

Examples of Dilation (1) 12/3/2018

Examples of Dilation (2) 12/3/2018

Duality Erosion and dilation are duals of each other with respect to set complementation and reflection 12/3/2018

Duality Erosion and dilation are duals of each other with respect to set complementation and reflection 12/3/2018

Duality Erosion and dilation are duals of each other with respect to set complementation and reflection 12/3/2018

Opening and Closing Opening generally smoothes the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions Closing tends to smooth sections of contours but it generates fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour 12/3/2018

Opening and Closing 12/3/2018

Opening 12/3/2018

Example: Opening 12/3/2018

Example: Closing 12/3/2018

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Duality of Opening and Closing Opening and closing are duals of each other with respect to set complementation and reflection 12/3/2018

The Properties of Opening and Closing Properties of Closing 12/3/2018

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The Hit-or-Miss Transformation 12/3/2018

Some Basic Morphological Algorithms (1) Boundary Extraction The boundary of a set A, can be obtained by first eroding A by B and then performing the set difference between A and its erosion. 12/3/2018

Example 1 12/3/2018

Example 2 12/3/2018

Some Basic Morphological Algorithms (2) Hole Filling A hole may be defined as a background region surrounded by a connected border of foreground pixels. Let A denote a set whose elements are 8-connected boundaries, each boundary enclosing a background region (i.e., a hole). Given a point in each hole, the objective is to fill all the holes with 1s. 12/3/2018

Some Basic Morphological Algorithms (2) Hole Filling 1. Forming an array X0 of 0s (the same size as the array containing A), except the locations in X0 corresponding to the given point in each hole, which we set to 1. 2. Xk = (Xk-1 + B) Ac k=1,2,3,… Stop the iteration if Xk = Xk-1 12/3/2018

Example 12/3/2018

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Some Basic Morphological Algorithms (3) Extraction of Connected Components Central to many automated image analysis applications. Let A be a set containing one or more connected components, and form an array X0 (of the same size as the array containing A) whose elements are 0s, except at each location known to correspond to a point in each connected component in A, which is set to 1. 12/3/2018

Some Basic Morphological Algorithms (3) Extraction of Connected Components Central to many automated image analysis applications. 12/3/2018

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Some Basic Morphological Algorithms (4) Convex Hull A set A is said to be convex if the straight line segment joining any two points in A lies entirely within A. The convex hull H or of an arbitrary set S is the smallest convex set containing S. 12/3/2018

Some Basic Morphological Algorithms (4) Convex Hull 12/3/2018

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Some Basic Morphological Algorithms (5) Thinning The thinning of a set A by a structuring element B, defined 12/3/2018

Some Basic Morphological Algorithms (5) A more useful expression for thinning A symmetrically is based on a sequence of structuring elements: 12/3/2018

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Some Basic Morphological Algorithms (6) Thickening: 12/3/2018

Some Basic Morphological Algorithms (6) 12/3/2018

Some Basic Morphological Algorithms (7) Skeletons 12/3/2018

Some Basic Morphological Algorithms (7) 12/3/2018

Some Basic Morphological Algorithms (7) 12/3/2018

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Some Basic Morphological Algorithms (7) 12/3/2018

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Some Basic Morphological Algorithms (8) Pruning 12/3/2018

Pruning: Example 12/3/2018

Pruning: Example 12/3/2018

Pruning: Example 12/3/2018

Pruning: Example 12/3/2018

Pruning: Example 12/3/2018

Some Basic Morphological Algorithms (9) Morphological Reconstruction 12/3/2018

Morphological Reconstruction: Geodesic Dilation 12/3/2018

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Morphological Reconstruction: Geodesic Erosion 12/3/2018

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Morphological Reconstruction by Dilation 12/3/2018

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Morphological Reconstruction by Erosion 12/3/2018

Opening by Reconstruction 12/3/2018

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Filling Holes 12/3/2018

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Border Clearing 12/3/2018

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Summary (1) 12/3/2018

Summary (2) 12/3/2018

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Gray-Scale Morphology 12/3/2018

Gray-Scale Morphology: Erosion and Dilation by Flat Structuring 12/3/2018

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Gray-Scale Morphology: Erosion and Dilation by Nonflat Structuring 12/3/2018

Duality: Erosion and Dilation 12/3/2018

Opening and Closing 12/3/2018

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Properties of Gray-scale Opening 12/3/2018

Properties of Gray-scale Closing 12/3/2018

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Morphological Smoothing Opening suppresses bright details smaller than the specified SE, and closing suppresses dark details. Opening and closing are used often in combination as morphological filters for image smoothing and noise removal. 12/3/2018

Morphological Smoothing 12/3/2018

Morphological Gradient Dilation and erosion can be used in combination with image subtraction to obtain the morphological gradient of an image, denoted by g, The edges are enhanced and the contribution of the homogeneous areas are suppressed, thus producing a “derivative-like” (gradient) effect. 12/3/2018

Morphological Gradient 12/3/2018

Top-hat and Bottom-hat Transformations The top-hat transformation of a grayscale image f is defined as f minus its opening: The bottom-hat transformation of a grayscale image f is defined as its closing minus f: 12/3/2018

Top-hat and Bottom-hat Transformations One of the principal applications of these transformations is in removing objects from an image by using structuring element in the opening or closing operation 12/3/2018

Example of Using Top-hat Transformation in Segmentation 12/3/2018

Granulometry Granulometry deals with determining the size of distribution of particles in an image Opening operations of a particular size should have the most effect on regions of the input image that contain particles of similar size For each opening, the sum (surface area) of the pixel values in the opening is computed 12/3/2018

Example 12/3/2018

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Textual Segmentation Segmentation: the process of subdividing an image into regions. 12/3/2018

Textual Segmentation 12/3/2018

Gray-Scale Morphological Reconstruction (1) Let f and g denote the marker and mask image with the same size, respectively and f ≤ g. The geodesic dilation of size 1 of f with respect to g is defined as The geodesic dilation of size n of f with respect to g is defined as 12/3/2018

Gray-Scale Morphological Reconstruction (2) The geodesic erosion of size 1 of f with respect to g is defined as The geodesic erosion of size n of f with respect to g is defined as 12/3/2018

Gray-Scale Morphological Reconstruction (3) The morphological reconstruction by dilation of a gray-scale mask image g by a gray-scale marker image f, is defined as the geodesic dilation of f with respect to g, iterated until stability is reached, that is, The morphological reconstruction by erosion of g by f is defined as 12/3/2018

Gray-Scale Morphological Reconstruction (4) The opening by reconstruction of size n of an image f is defined as the reconstruction by dilation of f from the erosion of size n of f; that is, The closing by reconstruction of size n of an image f is defined as the reconstruction by erosion of f from the dilation of size n of f; that is, 12/3/2018

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Steps in the Example Opening by reconstruction of the original image using a horizontal line of size 1x71 pixels in the erosion operation Subtract the opening by reconstruction from original image Opening by reconstruction of the f’ using a vertical line of size 11x1 pixels Dilate f1 with a line SE of size 1x21, get f2. 12/3/2018

Steps in the Example Calculate the minimum between the dilated image f2 and and f’, get f3. By using f3 as a marker and the dilated image f2 as the mask, 12/3/2018